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235 changes: 121 additions & 114 deletions docs/bibliography.bib

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80 changes: 40 additions & 40 deletions docs/src/Theory/Atmos/Microphysics.md
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Expand Up @@ -3,9 +3,9 @@
The `Microphysics.jl` module describes a 1-moment bulk parameterization of
cloud microphysical processes.
The module is based on the ideas of
[kessler1995](@cite),
[grabowski1998](@cite)
and [kaul2015](@cite).
[Kessler1995](@cite),
[Grabowski1998](@cite)
and [Kaul2015](@cite).

The cloud microphysics variables are expressed as specific humidities:
- `q_tot` - total water specific humidity,
Expand Down Expand Up @@ -78,12 +78,12 @@ With that said, the assumption about the shape of the particles is used three
|``m_e^{ice}`` | exponent in ``m(r)`` for ice | - | ``3`` | |
| | | | | |
|``r_0^{sno}`` | typical snow crystal radius | ``m`` | ``10^{-3} `` | |
|``m_0^{sno}`` | coefficient in ``m(r)`` for snow | ``kg`` | ``0.1 \, r_0^2`` | eq (6b) [grabowski1998](@cite) |
|``m_e^{sno}`` | exponent in ``m(r)`` for snow | - | ``2`` | eq (6b) [grabowski1998](@cite) |
|``a_0^{sno}`` | coefficient in ``a(r)`` for snow | ``m^2`` | ``0.3 \pi \, r_0^2`` | ``\alpha`` in eq(16b) [grabowski1998](@cite).|
|``m_0^{sno}`` | coefficient in ``m(r)`` for snow | ``kg`` | ``0.1 \, r_0^2`` | eq (6b) [Grabowski1998](@cite) |
|``m_e^{sno}`` | exponent in ``m(r)`` for snow | - | ``2`` | eq (6b) [Grabowski1998](@cite) |
|``a_0^{sno}`` | coefficient in ``a(r)`` for snow | ``m^2`` | ``0.3 \pi \, r_0^2`` | ``\alpha`` in eq(16b) [Grabowski1998](@cite).|
|``a_e^{sno}`` | exponent in ``a(r)`` for snow | - | ``2`` | |
|``v_0^{sno}`` | coefficient in ``v_{term}(r)`` for snow | ``\frac{m}{s}`` | ``2^{9/4} r_0^{1/4}`` | eq (6b) [grabowski1998](@cite) |
|``v_e^{sno}`` | exponent in ``v_{term}(r)`` for snow | - | ``0.25`` | eq (6b) [grabowski1998](@cite) |
|``v_0^{sno}`` | coefficient in ``v_{term}(r)`` for snow | ``\frac{m}{s}`` | ``2^{9/4} r_0^{1/4}`` | eq (6b) [Grabowski1998](@cite) |
|``v_e^{sno}`` | exponent in ``v_{term}(r)`` for snow | - | ``0.25`` | eq (6b) [Grabowski1998](@cite) |

where:
- ``\rho_{water}`` is the density of water,
Expand Down Expand Up @@ -112,15 +112,15 @@ where:
It would be great to replace the above simple power laws
with more accurate relationships.
For example:
[khvorostyanov2002](@cite)
[Khvorostyanov2002](@cite)
or
[karrer2020](@cite)
[Karrer2020](@cite)

## Assumed particle size distributions

The particle size distributions are assumed to follow
Marshall-Palmer distribution
[marshall1948](@cite)
[Marshall1948](@cite)
eq. 1:
```math
\begin{equation}
Expand Down Expand Up @@ -148,10 +148,10 @@ package and are shown in the table below.

| symbol | definition | units | default value | reference |
|-----------------|----------------------------------------------|--------------------|-------------------------------------------|------------|
|``n_{0}^{rai}`` | rain drop size distribution parameter | ``\frac{1}{m^4}`` | ``16 \cdot 10^6`` | eq (2) [marshall1948](@cite) |
|``n_{0}^{ice}`` | cloud ice size distribution parameter | ``\frac{1}{m^4}`` | ``2 \cdot 10^7`` | bottom of page 4396 [kaul2015](@cite) |
|``\mu^{sno}`` | snow size distribution parameter coefficient | ``\frac{1}{m^4}`` | ``4.36 \cdot 10^9 \, \rho_0^{\nu^{sno}}`` | eq (A1) [kaul2015](@cite) |
|``\nu^{sno}`` | snow size distribution parameter exponent | ``-`` | ``0.63`` | eq (A1) [kaul2015](@cite) |
|``n_{0}^{rai}`` | rain drop size distribution parameter | ``\frac{1}{m^4}`` | ``16 \cdot 10^6`` | eq (2) [Marshall1948](@cite) |
|``n_{0}^{ice}`` | cloud ice size distribution parameter | ``\frac{1}{m^4}`` | ``2 \cdot 10^7`` | bottom of page 4396 [Kaul2015](@cite) |
|``\mu^{sno}`` | snow size distribution parameter coefficient | ``\frac{1}{m^4}`` | ``4.36 \cdot 10^9 \, \rho_0^{\nu^{sno}}`` | eq (A1) [Kaul2015](@cite) |
|``\nu^{sno}`` | snow size distribution parameter exponent | ``-`` | ``0.63`` | eq (A1) [Kaul2015](@cite) |

The ``\lambda`` parameter is defined as
```math
Expand Down Expand Up @@ -199,19 +199,19 @@ They consist of:

| symbol | definition | units | default value | reference |
|----------------------------|-----------------------------------------------------------|--------------------------|------------------------|-----------|
|``C_{drag}`` | rain drop drag coefficient | - | ``0.55`` | ``C_{drag}`` is such that the mass averaged terminal velocity is close to [grabowski1996](@cite) |
|``C_{drag}`` | rain drop drag coefficient | - | ``0.55`` | ``C_{drag}`` is such that the mass averaged terminal velocity is close to [Grabowski1996](@cite) |
|``\tau_{cond\_evap}`` | cloud water condensation/evaporation timescale | ``s`` | ``10`` | |
|``\tau_{dep\_sub}`` | cloud ice deposition/sublimation timescale | ``s`` | ``10`` | |
|``\tau_{acnv}`` | cloud to rain water autoconversion timescale | ``s`` | ``10^3`` | eq (5a) [grabowski1996](@cite) |
|``q_{liq\_threshold}`` | cloud to rain water autoconversion threshold | - | ``5 \cdot 10^{-4}`` | eq (5a) [grabowski1996](@cite) |
|``r_{is}`` | threshold particle radius between ice and snow | ``m`` | ``62.5 \cdot 10^{-6}`` | abstract [harrington1995](@cite) |
|``E_{lr}`` | collision efficiency between rain drops and cloud droplets| - | ``0.8`` | eq (16a) [grabowski1998](@cite) |
|``E_{ls}`` | collision efficiency between snow and cloud droplets | - | ``0.1`` | Appendix B [rutledge1983](@cite) |
|``E_{ir}`` | collision efficiency between rain drops and cloud ice | - | ``1`` | Appendix B [rutledge1984](@cite) |
|``E_{is}`` | collision efficiency between snow and cloud ice | - | ``0.1`` | bottom page 3649 [morrison2008](@cite) |
|``E_{rs}`` | collision efficiency between rain drops and snow | - | ``1`` | top page 3650 [morrison2008](@cite) |
|``a_{vent}^{rai}, b_{vent}^{rai}`` | rain drop ventilation factor coefficients | - | ``1.5 \;``,``\; 0.53`` | chosen such that at ``q_{tot}=15 g/kg`` and ``T=288K`` the evap. rate is close to empirical evap. rate in [grabowski1996](@cite) |
|``a_{vent}^{sno}, b_{vent}^{sno}`` | snow ventilation factor coefficients | - | ``0.65 \;``,``\; 0.44``| eq (A19) [kaul2015](@cite) |
|``\tau_{acnv}`` | cloud to rain water autoconversion timescale | ``s`` | ``10^3`` | eq (5a) [Grabowski1996](@cite) |
|``q_{liq\_threshold}`` | cloud to rain water autoconversion threshold | - | ``5 \cdot 10^{-4}`` | eq (5a) [Grabowski1996](@cite) |
|``r_{is}`` | threshold particle radius between ice and snow | ``m`` | ``62.5 \cdot 10^{-6}`` | abstract [Harrington1995](@cite) |
|``E_{lr}`` | collision efficiency between rain drops and cloud droplets| - | ``0.8`` | eq (16a) [Grabowski1998](@cite) |
|``E_{ls}`` | collision efficiency between snow and cloud droplets | - | ``0.1`` | Appendix B [Rutledge1983](@cite) |
|``E_{ir}`` | collision efficiency between rain drops and cloud ice | - | ``1`` | Appendix B [Rutledge1984](@cite) |
|``E_{is}`` | collision efficiency between snow and cloud ice | - | ``0.1`` | bottom page 3649 [Morrison2008](@cite) |
|``E_{rs}`` | collision efficiency between rain drops and snow | - | ``1`` | top page 3650 [Morrison2008](@cite) |
|``a_{vent}^{rai}, b_{vent}^{rai}`` | rain drop ventilation factor coefficients | - | ``1.5 \;``,``\; 0.53`` | chosen such that at ``q_{tot}=15 g/kg`` and ``T=288K`` the evap. rate is close to empirical evap. rate in [Grabowski1996](@cite) |
|``a_{vent}^{sno}, b_{vent}^{sno}`` | snow ventilation factor coefficients | - | ``0.65 \;``,``\; 0.44``| eq (A19) [Kaul2015](@cite) |
|``K_{therm}`` | thermal conductivity of air | ``\frac{J}{m \; s \; K}``| ``2.4 \cdot 10^{-2}`` | |
|``\nu_{air}`` | kinematic viscosity of air | ``\frac{m^2}{s}`` | ``1.6 \cdot 10^{-5}`` | |
|``D_{vapor}`` | diffusivity of water vapor | ``\frac{m^2}{s}`` | ``2.26 \cdot 10^{-5}`` | |
Expand All @@ -220,7 +220,7 @@ They consist of:

The ventilation factor parameterizes the increase in the mass and heat exchange
for falling particles.
Following [seifert2006](@cite)
Following [Seifert2006](@cite)
eq. 24 the ventilation factor is defined as:
```math
\begin{equation}
Expand Down Expand Up @@ -261,7 +261,7 @@ F(r) = a_{vent} +
## Terminal velocity

The mass weighted terminal velocity ``v_t`` is defined following
[ogura1971](@cite):
[Ogura1971](@cite):
```math
\begin{equation}
v_t = \frac{\int_0^\infty n(r) \, m(r) \, v_{term}(r) \, dr}
Expand All @@ -285,9 +285,9 @@ Integrating over the assumed Marshall-Palmer distribution and using the
be size and flow dependent.
<!-- [drag_coefficient](https://www.grc.nasa.gov/www/K-12/airplane/dragsphere.html) -->
In general we should implement these terminal velocity parameterizations:
[khvorostyanov2002](@cite)
[Khvorostyanov2002](@cite)
or
[karrer2020](@cite)
[Karrer2020](@cite)

## Cloud water condensation/evaporation

Expand Down Expand Up @@ -326,14 +326,14 @@ where:
available condensation nuclei, turbulence intensity, etc.
See works by [prof Raymond Shaw](https://www.mtu.edu/physics/department/faculty/shaw/)
for hints.
In particular, [desai2019](@cite).
In particular, [Desai2019](@cite).

## Rain autoconversion

Rain autoconversion defines the rate of conversion form cloud liquid water
to rain water due to collisions between cloud droplets.
It is parameterized following
[kessler1995](@cite):
[Kessler1995](@cite):

```math
\begin{equation}
Expand All @@ -350,7 +350,7 @@ where:
This is the simplest possible autoconversion parameterization.
It would be great to implement others and test the impact on precipitation.
See for example
[wood2005](@cite)
[Wood2005](@cite)
Table 1 for other simple choices.

## Snow autoconversion
Expand All @@ -359,7 +359,7 @@ Snow autoconversion defines the rate of conversion form cloud ice to snow due
the growth of cloud ice by water vapor deposition.
It is defined as the change of mass of cloud ice for cloud ice particles
larger than threshold ``r_{is}``.
See [harrington1995](@cite)
See [Harrington1995](@cite)
for derivation.

```math
Expand All @@ -375,7 +375,7 @@ The ``\frac{dm}{dt}`` is obtained by solving the water vapor diffusion equation
in spherical coordinates and linking the changes in temperature at the drop
surface to the changes in saturated vapor pressure via the Clausius-Clapeyron
equation, following
[mason2010](@cite).
[Mason2010](@cite).

For the simplest case of spherical particles and not taking into account
ventilation effects:
Expand Down Expand Up @@ -421,7 +421,7 @@ Finally the snow autoconversion rate is computed as
For non-spherical particles the mass rate of growth
should be multiplied by a function depending on the particle aspect ratio.
For functions proposed for different crystal habitats see
[harrington1995](@cite) Appendix B.
[Harrington1995](@cite) Appendix B.

## Accretion

Expand Down Expand Up @@ -538,7 +538,7 @@ There are two additional assumptions that we make to integrate
- We assume that ``a(r_i, r_j) = \pi (r_i + r_j)^2``.
This corresponds to a geometric formulation of the collision kernel,
aka cylindrical formulation, see
[wang2006](@cite)
[Wang2006](@cite)
for discussion.

The eq.(\ref{eq:accr_sr1}) can then be integrated as:
Expand Down Expand Up @@ -699,21 +699,21 @@ const rain_param_set = RainParameterSet()
const ice_param_set = IceParameterSet()
const snow_param_set = SnowParameterSet()
# eq. 5d in [grabowski1996](@cite)
# eq. 5d in [Grabowski1996](@cite)
function terminal_velocity_empirical(q_rai::DT, q_tot::DT, ρ::DT, ρ_air_ground::DT) where {DT<:Real}
rr = q_rai / (DT(1) - q_tot)
vel = DT(14.34) * ρ_air_ground^DT(0.5) * ρ^-DT(0.3654) * rr^DT(0.1346)
return vel
end
# eq. 5b in [grabowski1996](@cite)
# eq. 5b in [Grabowski1996](@cite)
function accretion_empirical(q_rai::DT, q_liq::DT, q_tot::DT) where {DT<:Real}
rr = q_rai / (DT(1) - q_tot)
rl = q_liq / (DT(1) - q_tot)
return DT(2.2) * rl * rr^DT(7/8)
end
# eq. 5c in [grabowski1996](@cite)
# eq. 5c in [Grabowski1996](@cite)
function rain_evap_empirical(q_rai::DT, q::PhasePartition, T::DT, p::DT, ρ::DT) where {DT<:Real}
ts_neq = PhaseNonEquil_ρTq(param_set, ρ, T, q)
Expand Down
8 changes: 4 additions & 4 deletions docs/src/Theory/Common/SurfaceFluxes.md
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Expand Up @@ -16,7 +16,7 @@ This module provides a means to compute surface fluxes given several variables,

## References

- [businger1971](@cite)
- [nishizawa2018](@cite)
- [byun1990](@cite)
- [wyngaard1975](@cite)
- [Businger1971](@cite)
- [Nishizawa2018](@cite)
- [Byun1990](@cite)
- [Wyngaard1975](@cite)
2 changes: 1 addition & 1 deletion experiments/AtmosLES/bomex_model.jl
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Expand Up @@ -22,7 +22,7 @@
# 3) Collapsed experiment design
# 4) Updates to generally keep this in sync with master
[siebesma2003](@cite)
[Siebesma2003](@cite)
=#

using ArgParse
Expand Down
2 changes: 1 addition & 1 deletion experiments/AtmosLES/convective_bl_model.jl
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Expand Up @@ -5,7 +5,7 @@
# Convective Boundary Layer LES case (Kitamura et al, 2016).

## ### Convective Boundary Layer LES
## [nishizawa2018](@cite)
## [Nishizawa2018](@cite)
#
# To simulate the experiment, type in
#
Expand Down
4 changes: 2 additions & 2 deletions experiments/AtmosLES/dycoms.jl
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Expand Up @@ -83,7 +83,7 @@ function flux_radiation!(
DYCOMSRadiation <: RadiationModel
## References
- [stevens2005](@cite)
- [Stevens2005](@cite)
"""
struct DYCOMSRadiation{FT} <: RadiationModel
"mass absorption coefficient `[m^2/kg]`"
Expand Down Expand Up @@ -175,7 +175,7 @@ end
Initial Condition for DYCOMS_RF01 LES
## References
- [stevens2005](@cite)
- [Stevens2005](@cite)
"""
function init_dycoms!(problem, bl, state, aux, localgeo, t)
FT = eltype(state)
Expand Down
2 changes: 1 addition & 1 deletion experiments/AtmosLES/schar_scalar_advection.jl
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Expand Up @@ -24,7 +24,7 @@ struct EarthParameterSet <: AbstractEarthParameterSet end
const param_set = EarthParameterSet()

### Citation
# [schar2002](@cite)
# [Schar2002](@cite)

# ## [Initial Conditions]
function init_schar!(problem, bl, state, aux, localgeo, t)
Expand Down
4 changes: 2 additions & 2 deletions experiments/AtmosLES/stable_bl_model.jl
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Expand Up @@ -2,9 +2,9 @@
#=
# This experiment file establishes the initial conditions, boundary conditions,
# source terms and simulation parameters (domain size + resolution) for the
# GABLS LES case ([beare2006](@cite); [kosovic2000](@cite)).
# GABLS LES case ([Beare2006](@cite); [Kosovic2000](@cite)).
#
## [kosovic2000](@cite)
## [Kosovic2000](@cite)
#
# To simulate the experiment, type in
#
Expand Down
2 changes: 1 addition & 1 deletion src/Atmos/Model/AtmosModel.jl
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Expand Up @@ -919,7 +919,7 @@ see Chapter 10.4 in the provided reference below.
## References
- [toro2013riemann](@cite)
- [Toro2013](@cite)
"""
function numerical_flux_first_order!(
Expand Down
6 changes: 3 additions & 3 deletions src/Common/Spectra/power_spectrum_gcm.jl
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Expand Up @@ -8,8 +8,8 @@ The snapshots of these spectra should be averaged to obtain a time-average.
The input velocities must be interpolated to a Gaussian grid.
# References
- [wiin1967](@cite)
- [koshyk2001](@cite)
- [Wiin1967](@cite)
- [Koshyk2001](@cite)
# Arguments
- var_grid: variable (typically u or v) on a Gausian (lon, lat, z) grid to be transformed
Expand Down Expand Up @@ -73,7 +73,7 @@ end
- mass_weight: weight for mass-weighted calculations
# References
- [baer1972](@cite)
- [Baer1972](@cite)
"""
function power_spectrum_2d(::AtmosGCMConfigType, var_grid, mass_weight)
# initialize spherical mesh variables
Expand Down
2 changes: 1 addition & 1 deletion src/Common/SurfaceFluxes/SurfaceFluxes.jl
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Expand Up @@ -10,7 +10,7 @@
- exchange coefficients
## References
- [nishizawa2018](@cite)
- [Nishizawa2018](@cite)
"""
module SurfaceFluxes
Expand Down
8 changes: 4 additions & 4 deletions src/Common/SurfaceFluxes/UniversalFunctions.jl
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Expand Up @@ -85,11 +85,11 @@ c_h(uf::AUF) = c_h(uf.param_set, uf)
# Reference
- [nishizawa2018](@cite)
- [Nishizawa2018](@cite)
# Original research
- [businger1971](@cite)
- [Businger1971](@cite)
# Equations in reference:
Expand Down Expand Up @@ -226,7 +226,7 @@ end
Gryanik <: AbstractUniversalFunction{FT}
# References
- [gryanik2020](@cite)
- [Gryanik2020](@cite)
# Equations in reference:
Expand Down Expand Up @@ -309,7 +309,7 @@ end
Grachev <: AbstractUniversalFunction{FT}
# References
- [grachev2007sheba](@cite)
- [Grachev2007](@cite)
Equations in reference:
Expand Down
10 changes: 5 additions & 5 deletions src/Common/TurbulenceClosures/TurbulenceClosures.jl
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Expand Up @@ -511,15 +511,15 @@ $(DocStringExtensions.FIELDS)
# Smagorinsky Model Reference
See [smagorinsky1963](@cite)
See [Smagorinsky1963](@cite)
# Lilly Model Reference
See [lilly1962](@cite)
See [Lilly1962](@cite)
# Brunt-Väisälä Frequency Reference
See [durran1982](@cite)
See [Durran1982](@cite)
"""
struct SmagorinskyLilly{FT} <: TurbulenceClosureModel
Expand Down Expand Up @@ -637,7 +637,7 @@ $(DocStringExtensions.FIELDS)
# Reference
- [vreman2004](@cite)
- [Vreman2004](@cite)
"""
struct Vreman{FT} <: TurbulenceClosureModel
"Smagorinsky Coefficient [dimensionless]"
Expand Down Expand Up @@ -733,7 +733,7 @@ $(DocStringExtensions.FIELDS)
# Reference
See [vreugdenhil2018](@cite)
See [Vreugdenhil2018](@cite)
"""
struct AnisoMinDiss{FT} <: TurbulenceClosureModel
Expand Down
2 changes: 1 addition & 1 deletion src/Driver/SolverTypes/IMEXSolverType.jl
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Expand Up @@ -61,7 +61,7 @@ where `n` is now only the nonlinear tendency.
discretizing the original PDE directly.
### References
- [giraldo2013](@cite)
- [Giraldo2013](@cite)
"""
struct IMEXSolverType{DS, ST} <: AbstractSolverType
# The type of discrete splitting to apply to the right-hand side
Expand Down
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